EP1998435B1  Method and system for estimating rotor angular position and rotor angular velocity at low speeds or standstill  Google Patents
Method and system for estimating rotor angular position and rotor angular velocity at low speeds or standstill Download PDFInfo
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 EP1998435B1 EP1998435B1 EP08251107.2A EP08251107A EP1998435B1 EP 1998435 B1 EP1998435 B1 EP 1998435B1 EP 08251107 A EP08251107 A EP 08251107A EP 1998435 B1 EP1998435 B1 EP 1998435B1
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 H—ELECTRICITY
 H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
 H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMOELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
 H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
 H02P21/06—Rotor flux based control involving the use of rotor position or rotor speed sensors

 H—ELECTRICITY
 H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
 H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMOELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
 H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
 H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
 H02P21/18—Estimation of position or speed
Description
 This invention relates to rotor angular position and velocity sensing systems for mechanical shaft sensorless control of dynamoelectric machines, and more particularly to an improved system for resolving the position and velocity of a rotor for a dynamoelectric machine using an estimate of extended rotor flux.
 In some vehicles, including some aircraft, a motor may be utilized both as a motor and as a generator. Because of this dual function, the motor may be called a dynamoelectric machine. A typical motor comprises a stationary stator, and a rotating rotor. In some motors, it is necessary to detect a position of a rotor in order to sustain operation of the motor. Determining a rotor position typically requires a shaft position sensor. It is desirable to eliminate a mechanical shaft sensor to reduce cost and improve reliability.
 Some methods of sensorless rotor position detection include the back EMF method, which determines rotor position based on voltage, the signal injection method, which injects high frequencies into a system, and the method discussed in
U.S. Patent No. 7,072,790 which uses flux to determine rotor position. It is desirable to improve the methodU.S. Patent No. 7,072,790 for applications operating at low speeds or at a standstill.  The present invention relates to a method of estimating rotor angular position and rotor angular velocity for a dynamoelectric machine as claimed in claim 1, and to a control for estimating an initial rotor angular position and a rotor angular velocity for a dynamoelectric machine from a standstill as claimed in claim 8.
 A method and system for estimating an angular position and an angular velocity of a rotor in a dynamoelectric machine measures an AC current and a potential for each of a plurality of windings coupled to a stator of the dynamoelectric machine, transforms the measured currents and potentials to a stationary frame to produce transformed currents and transformed potentials, and processes the transformed currents and transformed potentials to produce a first intermediate signal and a second intermediate signal. The first intermediate signal and the second intermediate signal are crosscoupled and processed to obtain a first extended rotor flux value and a second extended rotor flux value. The first extended rotor flux value and the second extended rotor flux value are applied to a phase lock loop to derive an estimated rotor angular position and an estimated rotor angular velocity for the dynamoelectric machine.
 These and other features of the present invention can be best understood from the following specification and drawings, the following of which is a brief description, and which describe certain embodiments of the invention by way of example only.


Figure 1 illustrates a block diagram of a mechanical sensorless rotor angular position and velocity sensing system. 
Figure 2 illustrates a phasor diagram of electrical parameters related to extended rotor flux. 
Figure 3 illustrates a block diagram of operations performed within the system ofFigure 1 to calculate a first extended rotor flux value and a second extended rotor flux value. 
Figure 4 illustrates a block diagram of how a microprocessor ofFigure 1 uses a phase lock loop (PLL) to obtain an estimated rotor angular position and an estimated rotor angular velocity. 
Figure 5 illustrates how a stationary frame of the system ofFigure 1 aligns with multiple phases of AC. 
Figure 6 illustrates an initial stator voltage and an initial rotor position as a function of time.  As shown in
Figure 1 , the rotor angular position and velocity sensing system 10 comprises a motor 12 that is able to operate as a starter to start an engine 14, or as a generator to power a load (not shown). Because of this dual function, the motor 12 may be called a dynamoelectric machine. In one example, the motor 12 is a brushless motor that requires a controller to know a position of its rotor to operate.  To start the motor 12, an AC power supply 16 provides an AC voltage along supply lines 18 to a rotating exciter 19. In the example of
Figure 1 , the AC power supply 16 provides three phases of AC power, however it is understood that other numbers of phases of AC power could be provided. The rotating exciter is connected to a shaft 21 that is also connected to the motor 12 and the engine 14.  The AC voltage from the supply lines 18 induces an AC voltage along motor terminals 20a, 20b, and 20c. The induced voltage causes a current to flow through an output filter 22. A microprocessor 24 measures a voltage 26 and a current 28 from each of the terminals 20a, 20b, and 20c. A position and speed estimator 30 uses the voltage and current measurements to estimate a flux of the motor 12 and to estimate a rotor position 32 and a rotor angular velocity 34.
 Once the estimated rotor position 32 and estimated rotor angular velocity 34 have been calculated, an inverter 38 is turned ON. The microprocessor 24 processes the estimated rotor position 32 and estimated rotor angular velocity 34 to control a pulse width modulated (PWM) generator 36. Inverter 38 is coupled to the PWM generator 36 and converts a DC voltage from DC voltage supply lines 40 to AC. This voltage enables AC to flow through the output filter 22, which improves power quality by filtering out harmonics and reducing electromagnetic interference (EMI). The AC from the terminals 20a, 20b, and 20c then flows to a stator of the motor 12 to sustain operation of the motor 12.

Figure 1 illustrates how the microprocessor 24 processes the estimated rotor position 32 and estimated rotor angular velocity 34 to control the inverter 38. An abc to dq frame transformer 42 uses the estimated rotor position 32 to transform the current measurements 28 to a rotating dq frame to obtain current values I_{d} and Iq. A torque current profile generator 44 uses the estimated rotor angular velocity 34 to lookup reference current values I_{d}* and I_{q}*. Comparators 45 and 46 compare the transformed I_{d} and Iq values to reference current values I_{d}* and I_{q}* to determine differences ΔI_{d} and ΔI_{q} between the transformed values and the reference values.  Proportional and integral (PI) regulators 47 and 48 process the differences ΔI_{d} and ΔI_{q} using proportional and integral gains, and transmit an output signal to dq to alphabeta frame transformer 50, which converts the output into a stationary α β frame to produce V_{alpha}* and V_{beta}* signals which are transmitted to the PWM generator 36. The PWM generator then controls the inverter 38 accordingly to produce a desired AC voltage.
 The output filter 22 comprises an inductor and a capacitor (not shown) in each phase. An input current I_{invt} flows from the inverter 38 along the windings 23 a, 23b, and 23c to the output filter 22, and an output current I_{s} flows from the output filter 22 along the terminals 20a, 20b, and 20c to the motor 12. The current flowing through the capacitor can be calculated by the following equation:
$${\hat{I}}_{c}=C\frac{d{V}_{s}}{dt}$$  where Î_{c} is an estimated capacitor current; and
 V_{s} is one of the voltage measurements 26.
 where I_{s} is the calculated motor current; and
 I_{invt} is the inverter output current.
 The voltage measurements 26 and current measurements 28 are measured from each of the three terminals (20a, 20b, 20c) and each of the three windings (23a, 23b; 23c) in an abc frame. The current measurement 28 is a measurement of the inverter output current I_{invt}. A flux estimation is implemented in an alphabeta (αβ) stationary frame. The relationship between the αβ frame and the abc frame is described in the following equation:
$$\left[\begin{array}{c}{f}_{\alpha}\\ {f}_{\beta}\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}1& \frac{1}{2}& \frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& \frac{\sqrt{3}}{2}\end{array}\right]\left[\begin{array}{c}{f}_{a}\\ {f}_{b}\\ {f}_{c}\end{array}\right]$$  where f can be replaced with voltage, current, or flux;
 α, b, and c represent the phases of current on the terminals 20a, 20b, and 20c in the abc frame; and
 α and β represent axes of the αβ frame.
 The stationary αβ frame is a two phase frame and is a necessary step in calculating flux. Equation #3 is used to determine an αaxis voltage V_{α}, a βaxis voltage V_{β}, an αaxis current I_{α}, and a βaxis current I_{β}.
 The following equation can then be used to determine an extended rotor flux in the αβ stationary frame:
$$\left[\begin{array}{c}{\mathit{\lambda}}_{\mathit{ext\_\alpha}}\\ {\mathit{\lambda}}_{\mathit{ext\_\beta}}\end{array}\right]=\frac{1}{s}\left(\left[\begin{array}{c}{V}_{\alpha}\\ {V}_{\beta}\end{array}\right]\left[\begin{array}{cc}{R}_{s}& 0\\ 0& {R}_{s}\end{array}\right]\left[\begin{array}{c}{I}_{\alpha}\\ {I}_{\beta}\end{array}\right]\right)\left[\begin{array}{cc}{L}_{q}& 0\\ 0& {L}_{q}\end{array}\right]\left[\begin{array}{c}{I}_{\alpha}\\ {I}_{\beta}\end{array}\right]$$  where λ _{ ext_α} is an alpha extended rotor flux;
 λ _{ ext_β} is a beta extended rotor flux;
 R_{s} is a stator resistance;
 L_{q} is a qaxis inductance; and
 1/s is an integrator.
 where ω_{i} is a selected corner frequency.

Figure 2 illustrates a phasor diagram in the rotating dq frame.Figure 2 illustrates the relationship between extended rotor flux and back EMF.  A flux λ_{s} in the stator of the motor 12 is represented by a phasor 60. A stator current I_{s} is represented by a phasor 62. A stator potential V_{s} is represented by a phasor 64. A phasor 66 represents I_{s}*L_{q} where L_{q} is a qaxis rotor inductance. A vector sum of the phasor 60, representing λ_{s}, and the phasor 66, representing I_{s}*L_{q}, is an extended rotor flux λ_{ext}, which aligns with the daxis of the dq frame, and is represented by a phasor 67.
 A back electromotive force (EMF) E_{s} is represented by a phasor 68. As shown in
Figure 2 , the back EMF E_{s} is perpendicular to the stator flux λ_{s} . The back EMF E_{s} , represented by the phasor 68, is a vector sum of the stator potential V_{s} represented by phasor 64 and stator resistance potential drop I_{s}*R_{s} represented by a phasor 70, where R_{s} is the stator resistance.  An extended back electromotive force (EEMF), E_{ext} , in the stator is represented by a phasor 72, and aligns with the qaxis of the dq frame. I_{s}*X_{q} , where X_{q} is a qaxis stator reactance, is represented by a phasor 74. The extended back EMF represented by phasor 72 is a vector sum of E_{s} represented by phasor 68 and I_{s}*X_{q} represented by a phasor 74.

Figure 3 illustrates a block diagram of the flux estimation algorithm shown in equation #5. As shown inFigure 3 , a transformed measured current I_{α} for the α axis on a signal path 80 is multiplied by the stator resistance R_{s} 82 to produce I_{α} *R_{s} on a signal path 84. A summer 86 subtracts I_{α} * R_{s} on the signal path 84 from the transformed potential V _{α} on a signal path 88 to produce V _{α}(I_{α}*R_{s} ) on a signal path 90. V_{α} (I_{α} *R_{s} ) on the signal path 90 is multiplied by a$\frac{1}{s+{\omega}_{i}}$ first lag function 92 to produce first intermediate signal$\frac{1}{s+{\omega}_{i}}\left({V}_{\alpha}\left({I}_{\alpha}*{R}_{s}\right)\right)$ on a signal path 93.$\frac{1}{s+{\omega}_{i}}\left({V}_{\alpha}\left({I}_{\alpha}*{R}_{s}\right)\right)$ on the signal path 93 is multiplied by a$\frac{{\omega}_{i}}{s+{\omega}_{i}}$ second lag function 94 to produce$\frac{{\omega}_{i}}{s+{\omega}_{i}}\left({V}_{\alpha}\left({I}_{\alpha}*{R}_{s}\right)\right)$ on a signal path 95.  Additionally, a transformed measured current I _{β} for the βaxis on a signal path 96 is multiplied by the stator resistance R_{s} 98 to produce I_{β} *R_{s} on a signal path 100. A summer 102 subtracts I_{β} *R_{s} on the signal path 100 from the transformed potential V_{β} on a signal path 104 to produce V_{β}(I_{β}*R_{s} ) on a signal path 106. V_{β} (I_{β}*R_{s} ) on the signal path 106 is multiplied by the
$\frac{1}{s+{\omega}_{i}}$ first lag function 108 to produce second intermediate signal$\frac{1}{s+{\omega}_{i}}\left({V}_{\beta}\left({I}_{\beta}*{R}_{s}\right)\right)$ on a signal path 110.$\frac{1}{s+{\omega}_{i}}\left({V}_{\beta}\left({I}_{\beta}*{R}_{s}\right)\right)$ on the signal path 110 is multiplied by the$\frac{{\omega}_{i}}{s+{\omega}_{i}}$ second lag function 112 to produce$\frac{{\omega}_{i}}{s+{\omega}_{i}}\left({V}_{\beta}\left({I}_{\beta}*{R}_{s}\right)\right)$ on a signal path 114.  The transformed measured current I _{α} for the αaxis on the signal path 80 is also multiplied by a qaxis inductance L_{q} 116 to produce I _{α} *L_{q} on the signal path 118. A summer 120 subtracts I_{α}*L_{q} on the signal path 118 from
$\frac{1}{s+{\omega}_{i}}\left({V}_{\alpha}\left({I}_{\alpha}*{R}_{s}\right)\right)$ on the signal path 93 and adds$\frac{{\omega}_{i}}{s+{\omega}_{i}}\left({V}_{\beta}\left({I}_{\beta}*{R}_{s}\right)\right)$ from the signal path 114 to produce$$\frac{1}{s+{\omega}_{i}}\left({V}_{\alpha}\left({I}_{\alpha}*{R}_{s}\right)\right)+\frac{{\omega}_{i}}{{\left(s+{\omega}_{i}\right)}^{2}}\left({V}_{\beta}\left({I}_{\beta}*{R}_{s}\right)\right){I}_{\alpha}*{L}_{q}$$ which corresponds to the extended rotor flux on the αaxisλ _{ext_α} on the signal path 122. The "^"notation indicates that the extended rotor flux is an estimate based on measured values.  Additionally, the transformed measured current I_{β} for the βaxis on the signal path 96 is also multiplied by a qaxis inductance L_{q} 124 to produce I_{β}*L_{q} on the signal path 126. A summer 128 subtracts I_{β}*L_{q} on the signal path 126 from
$\frac{1}{s+{\omega}_{i}}\left({V}_{\beta}\left({I}_{\beta}*{R}_{s}\right)\right)$ on the signal path 110 and subtracts$\frac{{\omega}_{i}}{s+{\omega}_{i}}\left({V}_{\alpha}\left({I}_{\alpha}*{R}_{s}\right)\right)$ on the signal path 95 to produce$$\frac{1}{s+{\omega}_{i}}\left({V}_{\beta}\left({I}_{\beta}*{R}_{s}\right)\right)\frac{{\omega}_{i}}{{\left(s+{\omega}_{i}\right)}^{2}}\left({V}_{\alpha}\left({I}_{\alpha}*{R}_{s}\right)\right){I}_{\beta}*{L}_{q}$$ which corresponds to the extended rotor flux on the βaxisλ _{ est_β } on the signal path 130. Once again, the "^"notation indicates that the extended rotor flux is an estimate based on measured values.  As shown in
Figure 3 , the signal paths 95 and 114 crosscouple the signal paths 93 and 110.  The following equation can be used to describe the relationship between the extended rotor flux and the rotor position:
$$\left[\begin{array}{c}{\mathit{\lambda}}_{\mathit{ext\_\alpha}}\\ {\mathit{\lambda}}_{\mathit{ext\_\beta}}\end{array}\right]=\left\mathrm{\lambda}\right\left[\begin{array}{c}\mathrm{cos}\left(\theta \right)\\ \mathrm{sin}\left(\theta \right)\end{array}\right]$$  where θ is the rotor position; and
 λ is a flux amplitude.
 Using equation #6, it would be possible to use an arctangent function to calculate a rotor position. Another option is to used a phaselocked loop (PLL) to derive position and angular velocity information.

Figure 4 is a block diagram illustrating how the microprocessor 24 uses a phase lock loop (PLL) to improve an estimate of rotor angular position and rotor angular velocity. The estimated αaxis extended rotor fluxλ _{ ext_α } and the estimated βaxis extended rotor fluxλ _{ ext_β } are applied to the signal paths 122 and 130. A multiplier 132 multiplies the estimated αaxis extended rotor fluxλ _{ext_α} with a feedback signal on a signal path 134 from a sine function 136 to produce an αaxis multiplier output signal on a signal path 138. Likewise, a multiplier 140 multiplies the estimated βaxis extended rotor fluxλ _{ext_β} with a feedback signal on a signal path 142 from a cosine function 144 to produce a βaxis multiplier output signal on a signal path 146.  A summer 148 subtracts the αaxis multiplier output signal on the signal path 138 from the βaxis multiplier output signal on the signal path 146 to produce a difference signal on a signal path 150. A proportional and integral (PI) regulator function 152 multiplies the difference signal on the signal path 150 by the function
${K}_{p}+\frac{{K}_{i}}{s}$ to produce a PI output signal on a signal path 154. K_{i} is an integral gain of the PI function 152, and K_{p} is a proportional gain of the PI function 152. Both K_{i} and K_{p} are constants based on a design of the system 10 as shown inFigure 1 .  An integral function 156 multiplies the PI output signal on the signal path 154 by the function
$\frac{1}{s}$ to produce an integration output signal on a signal path 158. The integration output signal on the signal path 158 is also fed into the inputs of the sine function 136 and the cosine function 144 to provide the PLL.  A low pass filter (LPF) function 160 multiplies the PI output signal on the signal path 154 by a third lag function
$\frac{{\omega}_{c}}{s+{\omega}_{c}}$ to produce an estimated rotor angular velocity ω̂ on a signal line 162, where ω_{c} is a corner or cutoff frequency of the LPF function 160. A low pass filter associated with the LPF function 160 is used to smooth out the signal on the signal line 154.  The integration output signal on the signal path 158 is compensated by an offset Δθ to obtain a final estimated rotor angular position
θ̂ . The offset Δθ can be a lumpsum error of miscellaneous delays, including delays introduced by the lag functions 92, 108 ofFigure 3 , digital sampling delays introduced in measured voltage and current signals, and computation delays in the microprocessor 24 as shown inFigure 1 . A lookup table 164 may be used to compensate for this phase delay Δθ. The lookup table 164 generates a suitable phase delay Δθ on a signal path 166, and a summer 168 subtracts the phase delay Δθ from the integration output signal on the signal path 158 to produce the estimated rotor angular positionθ̂ on a signal path 170. 
Figure 5 illustrates how the αβ frame 173 comprises an αaxis 174 and a β axis 175 that are perpendicular to each other. The αβ frame 173 aligns with a first phase 178, a second phase 180 and a third phase 182 of the system 10. A rotor 172 rotates, and its displacement from the αaxis is shown by the angle θ 184, which is the rotor angular position to be estimated.  When the motor 12 is at a standstill, as magnetic flux in the motor 12 changes in magnitude, a voltage is induced on the motor terminals 20a, 20b, and 20c, which can be sensed by the microprocessor 24. The induced stator voltages in the αβ frame can be described by the following equation:
$${V}_{\alpha}=\frac{d{\mathit{\lambda}}_{s}}{dt}\mathrm{cos}\left({\theta}_{0}\right)$$ $${V}_{\beta}=\frac{d{\mathit{\lambda}}_{s}}{dt}\mathrm{sin}\left({\theta}_{0}\right)$$  where λ_{s} is a magnitude of stator flux; and
 θ_{0} is an initial rotor position angle at standstill.
 The measured voltage 26 can be transformed to an alphabeta frame. The transformed measured voltages V_{α} and V_{β} may be fed into the PLL as shown in
Figure 4 to obtain the initial position angle θ_{0} . In that case, the voltage V _{α} replaces the fluxλ̂ _{ext_α} on the signal path 122, and the voltage V _{β} replaces the fluxλ̂ _{est_β} on the signal path 130 inFigure 4 . 
Figure 6 illustrates an initial stator voltage and an initial rotor position as a function of time. During startup the rotating exciter 19 is powered on by the ac power supply 16 inFigure 1 . Graph 186 illustrates a linetoline voltage for each phase of the motor 12 as a function of time, and graph 188 illustrates an estimated rotor position as a function of time in the motor 12. The inverter 38 is OFF in the time periods shown in graphs 186 and 188. A voltage 190 corresponds to a V_{BC} linetoline voltage, a voltage 192 corresponds to a V_{CA} linetoline voltage, and a voltage 194 corresponds to a V_{AB} linetoline voltage. An estimated rotor position θ _{0} 200 corresponds to an angle of the rotor 172.  During an initial time period 196, the AC power supply 16 is OFF, and the three voltages 190, 192, and 194 are close to zero and the estimated rotor position θ_{0} 200 cannot be used to determine actual rotor position. Specifically, if each of the voltages does not exceed a certain threshold, the extended rotor flux values are not applied to the phase lock loop to derive an estimated rotor angular position and an estimated rotor angular velocity, and the estimated rotor angular position and estimated rotor angular velocity are designated as invalid. At time 198, the AC power supply 16 turns ON and current flows to the rotating exciter 19 through the supply line 18 in the system 10. During this period, an excitation magnetic field of the motor 12 is arising. The rising magnetic flux induces voltage at the terminals 20a, 20b, and 20c of the system 10. The magnitude of voltages 190, 192 and 194 is sufficient for the microprocessor 24 to be able to estimate rotor position θ_{0} 200. In graph 188, from time 198 to approximately time 202 the value of θ_{0} remains stable, and after time 202 the value starts to fluctuate due to a decaying voltage signal as shown in graph 186. This stable period demonstrates that a rotor position can be estimated from the voltages 190, 192, and 194 during the stable time period. If the rotor angular position cannot be determined within a predetermined period of time after the rotating exciter is turned on, the system indicates a fault condition. If the rotor angular position can be determined within a predetermined period of time after the rotating exciter is turned on, the inverter is turned on.
Claims (13)
 A method of estimating rotor angular position and rotor angular velocity for a dynamoelectric machine (12) comprising the steps of:(i) measuring an AC current (28) and a potential (26) for each of a plurality of windings coupled to a stator of the dynamoelectric machine;(ii) transforming the plurality AC currents and potentials to a stationary frame (αβ) to produce a first transformed current, a second transformed current, a first transformed potential, and a second transformed potential;(iii) processing the first transformed current and the first transformed potential, and processing the second transformed current and the second transformed potential to obtain a first intermediate signal (93) and a second intermediate signal (110);(iv) processing the first intermediate signal and the second intermediate signal to obtain a first extended rotor flux value (122) and a second extended rotor flux value (130); and(v) applying the first extended rotor flux value and the second extended rotor flux value to a phase lock loop (132158) to derive an estimated rotor angular position and an estimated rotor angular velocity for the dynamoelectric machine;wherein the stationary frame is a twophase αβ frame having an αaxis and a βtaxis, and the first transformed current is I_{α}, the second transformed current is I_{β} , the first transformed potential is V_{α} , the second transformed potential is V_{β} , the first extended rotor flux value corresponds to the αaxis, and the second extended rotor flux value corresponds to the βaxis; and
the step of processing the first transformed current and the first transformed potential, and processing the second transformed current and the second transformed potential to obtain a first intermediate signal and a second intermediate signal comprises the steps of:multiplying the first transformed current I_{α} and the second transformed current I_{β} by a resistance R_{s} of the stator to produce signals I_{α} *R_{s} ,I_{β} *R_{s} ;subtracting the signals I _{α}*R_{s} ,I _{β}*R_{s} from the first transformed potential V_{α} and the second transformed potential V_{β} to produce signals V _{α}I _{α}*R_{s} , V _{β} I _{β}*R_{s} ; andmultiplying the signals V _{α}I _{α}*R_{s} , V _{β}I _{β}*R_{s} by a first lag function$\frac{1}{s+{\omega}_{i}}\left(92,108\right),$ wherein ω _{i} is a selected corner frequency for the lag function and s is a Laplace operator, to produce first intermediate signal$\frac{1}{s+{\omega}_{i}}\left({V}_{\alpha}{I}_{\alpha}*{R}_{s}\right)$ and second intermediate signal$\frac{1}{s+{\omega}_{i}}\left({V}_{\beta}{I}_{\beta}*{R}_{s}\right)\left(110\right);$ multiplying the transformed currents Iα,I_{β} by a qaxis inductance L_{q} of the stator to produce signals I_{α}*L_{q},I_{β}*L_{q} ;characterised in that step (iv) comprises crosscoupling the first intermediate signal and the second intermediate signal to obtain the first extended rotor flux value (122) and the second extended rotor flux value (130); andin that the step of crosscoupling and processing the first intermediate signal and the second intermediate signal comprises the steps of:multiplying the first intermediate signal$\frac{1}{s+{\omega}_{i}}\left({V}_{\alpha}{I}_{\alpha}*{R}_{s}\right)$ and the second intermediate signal$\frac{1}{s+{\omega}_{i}}\left({V}_{\beta}{I}_{\beta}*{R}_{s}\right)\left(110\right)$ by a second lag function$\frac{{\omega}_{i}}{s+{\omega}_{i}}$ to produce signals$\frac{{\omega}_{i}}{{\left(s+{\omega}_{i}\right)}^{2}}\left({V}_{\alpha}{I}_{\alpha}*{R}_{s}\right)\left(95\right),\phantom{\rule{1em}{0ex}}\frac{{\omega}_{i}}{{\left(s+{\omega}_{i}\right)}^{2}}\left({V}_{\beta}{I}_{\beta}*{R}_{s}\right)\left(114\right);$ adding the signal$\frac{{\omega}_{i}}{{\left(s+{\omega}_{i}\right)}^{2}}\left({V}_{\beta}{I}_{\beta}*{R}_{s}\right)\left(114\right)$ to the first intermediate signal (93) and subtracting the signal I _{α}*L_{q} (118) to produce a signal$\frac{1}{s+{\omega}_{i}}\left({V}_{\alpha}{I}_{\alpha}*{R}_{s}\right)+\frac{{\omega}_{i}}{{\left(s+{\omega}_{i}\right)}^{2}}\left({V}_{\beta}{I}_{\beta}*{R}_{s}\right){I}_{\alpha}*{L}_{q}$ that corresponds to the first extended rotor flux value (λext_α; 122) andsubtracting the signal$\frac{{\omega}_{i}}{{\left(s+{\omega}_{i}\right)}^{2}}\left({V}_{\alpha}{I}_{\alpha}*{R}_{s}\right)$ from the second intermediate signal (110) and subtracting the signal I _{β}*L_{q} (126) to produce a signal$\frac{1}{s+{\omega}_{i}}\left({V}_{\beta}{I}_{\beta}*{R}_{s}\right)\frac{{\omega}_{i}}{{\left(s+{\omega}_{i}\right)}^{2}}\left({V}_{\alpha}{I}_{\alpha}*{R}_{s}\right){I}_{\beta}*{L}_{q}$ that corresponds to the second extended rotor flux value (λ_{extβ}; 130).  The method of claim 1, wherein the selected corner frequency ω_{i} is fixed.
 The method of claim 1 or 2, wherein the selected corner frequency ω_{i} is adjustable.
 The method of any preceding claim, wherein the step of applying the first extended rotor flux value and the second extended rotor flux value to a phase lock loop to derive an estimated rotor angular position and an estimated rotor angular velocity for the dynamoelectric machine comprises the steps of:multiplying the first extended rotor flux value with a sine function feedback signal to produce an αaxis multiplier output signal;multiplying the second extended rotor flux value with a cosine function feedback signal to produce an βaxis multiplier output signal;subtracting the αaxis multiplier output signal from the βaxis multiplier output signal to produce a difference signal;multiplying the difference signal by a proportional and integral regulator function
${K}_{p}+\frac{{K}_{i}}{s}$ to produce a PI output signal, wherein K_{p} is a constant value corresponding to a proportional gain of the proportional and integral regulator function, K_{i} is a constant value corresponding to an integral gain of the proportional and integral regulator function, and s is a Laplace operator;multiplying the PI output signal by an integral function$\frac{1}{s}$ to produce an integration output signal;multiplying the integration output signal by a sine function to produce the sine feedback signal; andmultiplying the integration output signal by a cosine function to produce the cosine feedback signal, wherein the estimated rotor angular position and the estimated rotor angular velocity for the dynamoelectric machine are derived from the proportional and integral regulator function output signal and the integration output signal.  The method of claim 4, further comprising the steps of:multiplying the proportional and integral regulator function output signal by a low pass filter function
$\frac{{\omega}_{c}}{s+{\omega}_{c}}$ to produce the estimated rotor angular velocity ω̂, where ω_{c} is a corner frequency of the low pass filter function;generating a delay compensation based on a value of the estimated rotor angular velocity; andsubtracting the delay compensation from the integration output signal to produce the estimated rotor angular position.  The method as recited in any preceding claim, further comprising the step of monitoring the potentials of the plurality of windings coupled to the stator of the dynamoelectric machine, wherein if the potentials do not exceed a certain threshold, the step of applying the first extended rotor flux value and the second extended rotor flux value to a phase lock loop to derive an estimated rotor angular position and an estimated rotor angular velocity for the dynamoelectric machine is not performed.
 The method of any preceding claim, further comprising the step of indicating a fault condition if the rotor angular position for the dynamoelectric machine cannot be determined within a predetermined period of time.
 A control for estimating an initial rotor angular position and a rotor angular velocity for a dynamoelectric machine (12) from a standstill comprising:a reference frame transformation function for transforming an AC potential (26) for each of a plurality of windings coupled to a stator of the dynamoelectric machine to a stationary frame (α_{}β) to produce a first transformed potential (V _{α}) and a second transformed potential (V_{β}), anda phase lock loop (132158) to derive an estimated rotor angular position (Θ) and an estimated rotor angular velocity for the dynamoelectric machine from the first transformed potential and the second transformed potential;wherein the control is arranged to estimate the initial rotor angular position and the rotor angular velocity according to the method of claim 1.
 The control of claim 8, wherein if the potential of each of the plurality of windings does not exceed a certain threshold, the control designates the estimated rotor angular position and estimated rotor angular velocity as invalid.
 The control of claim 8 or 9, wherein if the rotor angular position for the dynamoelectric machine cannot be determined within a predetermined period of time after a rotating exciter (19) is powered on, the system indicates a fault condition.
 The control of claim 8, 9 or 10, wherein if the rotor angular position for the dynamoelectric machine can be determined within a predetermined period of time after a rotating exciter (19) is powered on, an inverter is turned on.
 The control of any of claims 8 to 11, wherein the phase lock loop to derive an estimated rotor angular position value and an estimated rotor velocity value for the dynamoelectric machine from the first transformed potential and the second transformed potential comprises:a first multiplier (132) for multiplying the first transformed potential with a sine function feedback signal to produce an αaxis multiplier output signal;a second multiplier (140) for multiplying the second transformed potential with a cosine function feedback signal to produce an βaxis multiplier output signal;a first summer (148) for subtracting the αaxis multiplier output signal from the βaxis multiplier output signal to produce a difference signal;a proportional and integral regulator function (152) for multiplying the difference signal by a function
${K}_{p}+\frac{{K}_{i}}{s}$ to produce a PI output signal, wherein K_{p} is a constant value corresponding to a proportional gain of the proportional and integral regulator function, K_{i} is a constant value corresponding to an integral gain of the proportional and integral regulator function, and s is a Laplace operator;an integral function (156) for multiplying the PI output signal by an integral function$\frac{1}{s}$ to produce an integration output signal; sa sine function (136) for multiplying the integration output signal by a sine function to produce the sine feedback signal; anda cosine function (144) for multiplying the integration output signal by a cosine function to produce the cosine feedback signal, wherein the estimated rotor angular position and the estimated rotor angular velocity for the dynamoelectric machine are derived from the proportional and integral regulator function output signal and the integration output signal.  The control of claim 12, further comprising:a low pass filter (160) for filtering the PI output signal by a low pass filter function
$\frac{{\omega}_{c}}{s+{\omega}_{c}}$ to produce the estimated rotor angular velocity, where ω _{c} is a corner frequency of the low pass filter function;a lookup table (164) for generating a delay compensation based on a value of the estimated rotor angular velocity; anda second summer (168) for subtracting the delay compensation from the integration output signal to produce the estimated rotor angular position.
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